Question: Simplify the following expression: $k = \dfrac{15xy}{15y^2 - 25xy} + \dfrac{10y^2 - 15y}{15y^2 - 25xy}$ You can assume $x,y,z \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{15xy + 10y^2 - 15y}{15y^2 - 25xy}$ The numerator and denominator have a common factor of $5y$, so we can simplify $k = \dfrac{3x + 2y - 3}{3y - 5x}$